Axel van de Walle, Chirranjeevi Balaji Gopal, Steve Demers, Qijun Hong, Adam Kowalski, Ljubomir Miljacic, Gregory Pomrehn, Pratyush Tiwary
We present a simple and general method to generate a set of basis functions suitable for parametrizing the anisotropy of a given physical property in the presence of symmetry constraints. This mathematical tool has direct applications in various fields, for instance, to parametrize the orientation-dependence of interface energies or to represent the so-called constituent strain elastic energy of superlattice structures in the long wavelength limit. The proposed method can be easily implemented using generic linear algebra operations without having consider many different subcases that depend on the point group symmetry considered. The method exploits a direct correspondence between spherical harmonics and polynomial functions of a unit vectors expressed in tensor notation. The method has been implemented in the "gencs" code of the Alloy Theoretic Automated Toolkit (ATAT).
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http://arxiv.org/abs/1301.0168
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